Computer Organization and Design Instruction Sets - 2 Montek Singh Feb 10-12, 2016 Lecture 5

Today More MIPS instructions Reading signed vs. unsigned instructions larger constants accessing memory branches and jumps multiply, divide comparisons logical instructions Reading Book Chapter 2.1-2.7 Study the inside green flap (“Green Card”)

Recap: MIPS Instruction Formats All MIPS instructions fit into a single 32-bit word Every instruction includes various “fields”: a 6-bit operation or “OPCODE” specifies which operation to execute (fewer than 64) up to three 5-bit OPERAND fields each specifies a register (one of 32) as source/destination embedded constants also called “literals” or “immediates” 16-bits, 5-bits or 26-bits long sometimes treated as signed values, sometimes unsigned There are three basic instruction formats: R-type, 3 register operands (2 sources, destination) OP rs rt rd shamt func I-type, 2 register operands, 16-bit constant OP rs rt 16-bit constant J-type, no register operands, 26-bit constant OP 26-bit constant

Working with Constants Immediate instructions allow constants to be specified within the instruction Examples add 2000 to register $5 addi $5, $5, 2000 subtract 60 from register $5 addi $5, $5, -60 … no subi instruction! logically AND $5 with 0x8723 and put the result in $7 andi $7, $5, 0x8723 put the number 1234 in $10 addi $10, $0, 1234 But… these constants are limited to 16 bits only! Range is [-32768…32767] if signed, or [0…65535] if unsigned

constant field, indicating -3 as second operand Recap: ADDI addi instruction: adds register contents, signed-constant: 1 I-type: OP = 0x08, dictating addi rt = 9, Reg[9] destination constant field, indicating -3 as second operand (sign-extended!) rs = 11, Reg[11] source Symbolic version: addi $9, $11, -3 addi rt, rs, imm: Reg[rt] = Reg[rs] + sxt(imm) sign extention pads the sign to make the imm into a 32-bit signed number: 11111111111111111111111111111101 “Add the contents of rs to const; store result in rt”

ADDIU: Signed vs. Unsigned Constants addiu instruction: adds register to unsigned-constant: 1 I-type: OP = 0x09, dictating addiu rt = 9, Reg[9] destination constant field, indicating 65533 as second operand (zero-extended!) rs = 11, Reg[11] source Symbolic version: addiu $9, $11, 65533 The imm is 0-padded into a 32-bit unsigned (+ve) number: 00000000000000001111111111111101 addiu rt, rs, imm: Reg[rt] = Reg[rs] + (imm) “Add the contents of rs to const; store result in rt” Also: All logical operations are always “unsigned”, so always zero-extended

Logical operations: zero extension For logical operations, immediates are zero padded andi, ori, xori Why? because logical operations are bitwise values are not treated as arithmetic quantities … … but only as bit patterns Example: andi $1, $1, 0xffff results in $1  $1 & 0x0000ffff Also: unsigned versions of arithmetic instructions addiu, sltiu, etc. pad zeros to the left of the 16-bit immediate

How About Larger Constants? Problem: How do we work with bigger constants? Example: Put the 32-bit value 0x5678ABCD in $5 CLASS: How will you do it? One Solution: put the upper half (0x5678) into $5 then shift it left by 16 positions (0x5678 0000) now “add” the lower half to it (0x5678 0000 + 0xABCD) addi $5, $0, 0x5678 sll $5, $5, 16 addi $5, $5, 0xABCD One minor problem with this: addi can mess up by treating the constants are signed use addiu or ori instead

How About Larger Constants? Observation: This sequence is very common! so, a special instruction was introduced to make it shorter the first two (addi + sll) combo is performed by lui “load upper immediate” puts the 16-bit immediate into the upper half of a register Example: Put the 32-bit value 0x5678ABCD in $5 lui $5, 0x5678 ori $5, $5, 0xABCD

How About Larger Constants? Look at this in more detail: “load upper immediate” lui $5, 0x5678 // 0101 0110 0111 1000 in binary Then must get the lower order bits right ori $5, $5, 0xABCD // 1010 1011 1100 1101 0101011001111000 0000000000000000 Reminder: In MIPS, Logical Immediate instructions (ANDI, ORI, XORI) do not sign-extend their constant operand 0101011001111000 0000000000000000 0000000000000000 1010101111001101 ori 0101011001111000 1010101111001101

Accessing Memory MIPS is a “load-store” architecture Control Unit Data all operands for ALU instructions are in registers or immediate cannot directly add values residing in memory must first bring values into registers from memory (called LOAD) must store result of computation back into memory (called STORE) Control Unit Data Path registers MEMORY control status instructions data address

MIPS Load Instruction Load instruction is I-type Does the following: takes the value stored in register $rs adds to it the immediate value (signed) this is the address where memory is looked up value found at this address in memory is brought in and stored in register $rt OP rs rt 16-bit signed constant I-type: lw rt, imm(rs) Meaning: Reg[rt]= Mem[Reg[rs] + sign-ext(imm)] Abbreviation: lw rt,imm for lw rt, imm($0)

MIPS Store Instruction Store instruction is also I-type Does the following: takes the value stored in register $rs adds to it the immediate value (signed) this is the address where memory is accessed reads the value from register $rt and writes it into the memory at the address computed OP rs rt 16-bit signed constant I-type: sw rt, imm(rs) Meaning: Mem[Reg[rs] + sign-ext(imm)] = Reg[rt] Abbreviation: sw rt,imm for sw rt, imm($0)

MIPS Memory Addresses lw and sw read whole 32-bit words so, addresses computed must be multiples of 4 Reg[rs] + sign-ext(imm) must end in “00” in binary otherwise: runtime exception There are also byte-sized flavors of these instructions lb (load byte) sb (store byte) work the same way, but their addresses do not have to be multiples of 4

Storage Conventions Data stored in memory Example addresses in memory are assigned at compile time data values must be “loaded” into registers first operations done on registers result stored in memory Example assume compiler has assigned these memory addresses int x, y; y = x + 37; lw $t0, 0x1008($0) addiu $t0, $t0, 37 sw $t0, 0x100C($0) translates to: Compilation approach: LOAD, COMPUTE, STORE choice of $t0 is arbitrary 1000: n 1004: r 1008: x 100C: y 1010:

MIPS Branch Instructions MIPS branch instructions provide a way of conditionally changing the PC to some nearby location... OPCODE rs rt 16-bit signed constant I-type: if (REG[RS] == REG[RT]) { PC = PC + 4 + 4*offset; } beq rs, rt, label # Branch if equal if (REG[RS] != REG[RT]) { PC = PC + 4 + 4*offset; } bne rs, rt, label # Branch if not equal Notice on memory references offsets are multiplied by 4, so that branch targets are restricted to word boundaries. NB: Branch targets are specified relative to the next instruction (which would be fetched by default). The assembler hides the calculation of these offset values from the user, by allowing them to specify a target address (usually a label) and it does the job of computing the offset’s value. The size of the constant field (16-bits) limits the range of branches.

MIPS Jumps The range of MIPS branch instructions is limited to approximately  32K instructions ( 128K bytes) from the branch instruction. To branch farther: an unconditional jump instruction is used. Instructions: j label # jump to label (PC = PC[31-28] << 28 || CONST[25:0]*4) lower 28 bits are the const * 4 upper 4 bits are from the current PC value jal label # jump to label and store PC+4 in $31 jr $t0 # jump to address specified by register’s contents jalr $t0, $ra # jump to address specified by first register’s contents and store PC+4 in second register Formats: J-type: used for j OP = 2 26-bit constant J-type: used for jal OP = 3 26-bit constant R-type, used for jr OP = 0 rs func = 8 rs rd R-type, used for jalr OP = 0 func = 9

Multiply and Divide Slightly more complicated than add/subtract multiply: product is twice as long! if A, B are 32-bit long, A * B is how many bits? divide: dividing integer A by B gives two results! quotient and remainder Solution: two new special-purpose registers “Hi” and “Lo”

Multiply MULT instruction To access result, use two new instructions mult rs, rt Meaning: multiply contents of registers $rs and $rt, and store the (64-bit result) in the pair of special registers {hi, lo} hi:lo = $rs * $rt upper 32 bits go into hi, lower 32 bits go into lo To access result, use two new instructions mfhi: move from hi mfhi rd move the 32-bit half result from hi to $rd mflo: move from lo mflo rd move the 32-bit half result from lo to $rd

Divide DIV instruction To access result, use mfhi and mflo div rs, rt Meaning: divide contents of register $rs by $rt, and store the quotient in lo, and remainder in hi lo = $rs / $rt hi = $rs % $rt To access result, use mfhi and mflo NOTE: There are also unsigned versions multu divu

Now we can do a real program: Factorial... Synopsis (in C): Input in n, output in ans r1, r2 used for temporaries assume n is small int n, ans, r1, r2; r1 = 1; r2 = n; while (r2 != 0) { r1 = r1 * r2; r2 = r2 – 1; } ans = r1; MIPS code, in assembly language: n: .word 123 ans: .word 0 ... addi $t0, $0, 1 # t0 = 1 lw $t1, n($0) # t1 = n loop: beq $t1, $0, done # while (t1 != 0) mult $t0, $t1 # hi:lo = t0 * t1 mflo $t0 # t0 = t0 * t1 addi $t1, $t1, -1 # t1 = t1 - 1 j loop # Always loop back done: sw $t0, ans($0) # ans = r1

Comparison: slt, slti slt = set-if-less-than slt rd, rs, rt $rd = ($rs < $rt) // “1” if true and “0” if false slti = set-if-less-than-immediate slt rt, rs, imm $rt = ($rs < sign-ext(imm)) also unsigned flavors sltu sltiu

Logical Instructions Boolean operations: bitwise on all 32 bits AND, OR, NOR, XOR and, andi or, ori nor // Note: There is no nori xor, xori Examples: and $1, $2, $3 $1 = $2 & $3 xori $1, $2, 0xFF12 $1 = $2 ^ 0x0000FF12 See all in textbook!

Summary - 1

Summary - 2

MIPS Instruction Decoding Ring Top table summarizes opcodes Bottom table summarizes func field if opcode is 000000 OP 000 001 010 011 100 101 110 111 func j jal beq bne addi addiu slti sltiu andi ori xori lui lw sw func 000 001 010 011 100 101 110 111 sll srl sra sllv srlv srav jr jalr mult multu div divu add addu sub subu and or xor nor slt sltu

Summary We will use a subset of MIPS instruction set in this class Sometimes called “miniMIPS” All instructions are 32-bit 3 basic instruction formats R-type - Mostly 2 source and 1 destination register I-type - 1-source, a small (16-bit) constant, and a destination register J-type - A large (26-bit) constant used for jumps Load/Store architecture 31 general purpose registers, one hardwired to 0, and, by convention, several are used for specific purposes. ISA design requires tradeoffs, usually based on History, Art, Engineering Benchmark results